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- John Terilla
- 2008

Given a differential Batalin-Vilkovisky algebra (V,Q,∆, ·), the associated odd differential graded Lie algebra L := (V,Q + ∆, [ , ]) is always smooth formal. The more interesting consideration is whether the quantum dgLa L~ := (V [[~]],Q+ ~∆, [ , ]) is smooth formal. When it is (for example when a Q-∆ version of the ∂-∂ Lemma holds) there is a… (More)

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability… (More)

- Vladimir E. Korepin, John Terilla
- Quantum Information Processing
- 2002

Shannon’s fundamental coding theorems relate classical information theory to thermodynamics. More recent theoretical work has been successful in relating quantum information theory to thermodynamics. For example, Schumacher proved a quantum version of Shannon’s 1948 classical noiseless coding theorem. In this note, we extend the connection between quantum… (More)

This note defines cones in homotopy probability theory and demonstrates that a cone over a space is a reasonable replacement for the space. The homotopy Gaussian distribution in one variable is revisited as a cone on the ordinary Gaussian.

We derive an L∞ structure associated to a polarized quantum background and characterize the obstructions to finding a versal solution to the quantum master equation (QME). We illustrate how symplectic field theory (SFT) is an example of a polarized quantum background and discuss the L∞ structure in the SFT context. The discussion may be summarized as… (More)

We introduce the concept of a quantum background and a functor QFT. In the case that the QFT moduli space is smooth formal, we construct a flat quantum superconnection on a bundle over QFT which defines algebraic structures relevant to correlation functions in quantum field theory. We go further and identify chain level generalizations of correlation… (More)

- John Terilla, John Terilla
- 2009

We describe a step toward quantizing deformation theory. The L∞ operad is encoded in a Hochschild cocyle ◦1 in a simple universal algebra (P, ◦0). This Hochschild cocyle can be extended naturally to a star product ⋆ = ◦0+~◦1+~ 2 ◦2+ · · · . The algebraic structure encoded in ⋆ is the properad Ω(coFrob) which, conjecturally, controls a quantization of… (More)

Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential BatalinVilkovisky algebra. Moreover, if A is an A∞ algebra, then TA is a commutative BV∞ algebra. 1. Main Statement Let (A, dA) be a complex over a commutative ring R. Our convention is… (More)

- John Terilla
- 2008

The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are identified using subalgebras of a deformed Jacobian ring.

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability… (More)